Final answer:
The maximum non-relativistic speed of electrons accelerated by a 40 kV volt potential in an X-ray tube is approximately 1.2 × 10⁷ m/s (a). This is calculated using the kinetic energy formula that equates the energy gained from the voltage to the kinetic energy of the electron.
Step-by-step explanation:
The question pertains to the speed of electrons accelerated by a voltage in an X-ray tube. When electrons are accelerated through an electric potential, they gain kinetic energy equivalent to the work done by the electric field, which can be calculated using the energy conversion from electric potential energy to kinetic energy. The formula to determine the maximum speed (v) of an electron non-relativistically, after being accelerated through a voltage (V), is given by the equation KE = ½ mv² = qV, where KE is the kinetic energy of the electron, m is the mass of an electron (9.11 × 10⁻³¹ kg), q is the charge of an electron (1.602 × 10⁻ C), and V is the voltage.
In this case, with an accelerating voltage of 40 kV (or 40,000 volts), we can calculate the maximum speed of the electrons as follows:
- First, convert the voltage to joules: 40 kV = 40,000 V × 1.602 × 10⁻ C/V = 6.408 × 10⁻ J.
- Then, solve for the maximum speed using the equation: ½ mv² = qV. Rearranging for v gives us v = √(2qV/m).
- Plugging in the known values gives us v = √(2 × 1.602 × 10⁻ C × 40,000 V / 9.11 × 10⁻³¹ kg).
- Calculating the above expression gives us a maximum speed of approximately 1.2 × 10⁷ m/s, which corresponds to answer choice (a).